Title: Bayesian Approaches to State and Parameter Estimation
Abstract: Inverse problems are ubiquitous in the natural sciences: data from the physical world is observed and used to inform the state or parameters of a particular system. Many of these types of problems, however, are known to not posses unique solutions or may be unstable to small perturbations in data. Furthermore, errors in measurements and experiments further create uncertainty in the subsequent estimates that are produced. In this talk we explore the difficulties that can arise in certain inverse problems and how various approaches to Bayesian statistics can be used to leverage uncertainties to produce more accurate estimates and better calibrated forecasts.